|
|
|
Recent
Issues
|
|
Volume 53
|
1
|
2
|
3
|
4
|
|
Volume 52
|
1
|
2
|
3
|
4
|
|
Volume 51
|
1
|
2
|
3
|
4
|
|
Volume 50
|
1
|
2
|
3
|
4
|
|
Volume 49
|
1
|
2
|
3
|
4
|
|
|
Vietnam
Journal of Mathematics 39:1 (2011) 1-17
|
|
A Type of Markov Approximation of Random Fields on
a Homogeneous Tree
and a Class
of Small Deviation Theorems
|
|
Kangkang Wang and
Mingxing Zhu
|
|
Abstract. In this paper, a class of small deviation
theorems for an arbitrary bivariate function are introduced by introducing
the sample relative entropy rate as a measure of deviation between the
arbitrary random field and the Markov chains field on the
homogeneous tree. As corollaries, a class of small deviation theorems for
the frequencies of states ordered couples and a Shannon-McMillan
approximation theorem for arbitrary ran-dom fields on the homogeneous
tree are obtained.
|
|
2000 Mathematics Subject Classification: 60F15.
|
|
Keywords: Shannon-McMillan theorem, the homogeneous
tree, arbitrary random field, Markov random field, sample
relative entropy density.
|
|
|
|
Established
by Vietnam Academy of Science and Technology &
Vietnam Mathematical Society
Published by
Springer since January 2013
|
|
